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In this paper we consider the problem of finding the minimizations of the sumof two convex functions and the composition of another convex function with acontinuous linear operator. With the idea of coordinate descent, we design astochastic coordinate descent primal-dual splitting algorithm with dynamicstepsize. Based on randomized Modified Krasnosel'skii-Mann iterations and thefirmly nonexpansive properties of the proximity operator, we achieve theconvergence of the proposed algorithms. Moreover, we give two applications ofour method.

A stochastic coordinate descent primal-dual algorithm with dynamic stepsize for large-scale composite optimization